### Abstract

We propose a new algorithm for numerical solutions of constrained nonlinear optimal control problems, based on constrained LQ problems. The proposed algorithm is described as follows. First, we approximate the constrained nonlinear optimal control problems by the Taylor expansion technique, resulting in the standard LQ problems, but with linearized constraints. Then, by making use of penalty function methods, we construct the augmented LQ problem, which is one of unconstrained optimal control problems, and therefore we can easily obtain the optimal solution of the augmented LQ problem by Riccati transformation. Finally, repeating the above procedure with a certain type of filter, we ventually obtain the numerical solutions for constrained nonlinear optimal control problems. The effectiveness is demonstrated through simulation.

Original language | English |
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Title of host publication | Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009 |

Pages | 176-180 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

Event | 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009 - Okayama Duration: 2009 Mar 26 → 2009 Mar 29 |

### Other

Other | 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009 |
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City | Okayama |

Period | 09/3/26 → 09/3/29 |

### Keywords

- Computational method
- Constrained nonlinear optimal control problem
- LQ problem
- Penalty function

### ASJC Scopus subject areas

- Computer Networks and Communications
- Electrical and Electronic Engineering

### Cite this

*Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009*(pp. 176-180). [4919267] https://doi.org/10.1109/ICNSC.2009.4919267

**A constrained LQ approach to numerical solutions for constrained nonlinear optimal control problems.** / Imae, Joe; Ando, Tomonari; Kobayashi, Tomoaki; Zhai, Guisheng.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009.*, 4919267, pp. 176-180, 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009, Okayama, 09/3/26. https://doi.org/10.1109/ICNSC.2009.4919267

}

TY - GEN

T1 - A constrained LQ approach to numerical solutions for constrained nonlinear optimal control problems

AU - Imae, Joe

AU - Ando, Tomonari

AU - Kobayashi, Tomoaki

AU - Zhai, Guisheng

PY - 2009

Y1 - 2009

N2 - We propose a new algorithm for numerical solutions of constrained nonlinear optimal control problems, based on constrained LQ problems. The proposed algorithm is described as follows. First, we approximate the constrained nonlinear optimal control problems by the Taylor expansion technique, resulting in the standard LQ problems, but with linearized constraints. Then, by making use of penalty function methods, we construct the augmented LQ problem, which is one of unconstrained optimal control problems, and therefore we can easily obtain the optimal solution of the augmented LQ problem by Riccati transformation. Finally, repeating the above procedure with a certain type of filter, we ventually obtain the numerical solutions for constrained nonlinear optimal control problems. The effectiveness is demonstrated through simulation.

AB - We propose a new algorithm for numerical solutions of constrained nonlinear optimal control problems, based on constrained LQ problems. The proposed algorithm is described as follows. First, we approximate the constrained nonlinear optimal control problems by the Taylor expansion technique, resulting in the standard LQ problems, but with linearized constraints. Then, by making use of penalty function methods, we construct the augmented LQ problem, which is one of unconstrained optimal control problems, and therefore we can easily obtain the optimal solution of the augmented LQ problem by Riccati transformation. Finally, repeating the above procedure with a certain type of filter, we ventually obtain the numerical solutions for constrained nonlinear optimal control problems. The effectiveness is demonstrated through simulation.

KW - Computational method

KW - Constrained nonlinear optimal control problem

KW - LQ problem

KW - Penalty function

UR - http://www.scopus.com/inward/record.url?scp=70349095544&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349095544&partnerID=8YFLogxK

U2 - 10.1109/ICNSC.2009.4919267

DO - 10.1109/ICNSC.2009.4919267

M3 - Conference contribution

AN - SCOPUS:70349095544

SN - 9781424434923

SP - 176

EP - 180

BT - Proceedings of the 2009 IEEE International Conference on Networking, Sensing and Control, ICNSC 2009

ER -